A conducting wire has length `L_(1)` and diameter `d_(1)`. After stretching the same wire length becomes `L_(2)` and diameter `d_(2)`, The ratio of resistances before and after stretching is

Options

A. `d_(2)^(4):d_(1)^(4)`
B. `d_(1)^(4) :d_(2)^(4)`
C. `d_(2)^(2) :d_(1)^(2)`
D. `d_(1)^(2): d_(2)^(2)`

Answer

B

Explanation

Data :
`kl_(1) A l_(1) =l_(1)` ltbr `d_(1)=d _(1)`
`therefore r_(1)=r_(1)`
`r_(2)=r_(2)`
`(R_(1))/(R_(2))=?`
Now
`(R_(1))/(R_(2))=((r_(1))/(r_(2)))^(4)= ((d_(1))/(d_(2)))^(4)`
`(R_(1))/R_(2)=(d^(4))/(d_(2)^(4))`